A novel extension of Generalized Low-Rank Approximation of Matrices based on multiple-pairs of transformations

Dimension reduction is a main step in learning process which plays a essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can apply to vector data. This means that for higher order data like matrices or more generally tensors, data should be fold to a vector. By this folding, the probability of overfitting is increased and also maybe some important spatial features are ignored. Then, to tackle these issues, methods are proposed which work directly on data with their own format like GLRAM, MPCA, and MLDA. In these methods the spatial relationship among data are preserved and furthermore, the probability of overfitiing has fallen. Also the time and space complexity are less than vector-based ones. Having said that, because of the less parameters in multilinear methods, they have a much smaller search space to find an optimal answer in comparison with vector-based approach. To overcome this drawback of multilinear methods like GLRAM, we proposed a new method which is a general form of GLRAM and by preserving the merits of it have a larger search space. We have done plenty of experiments to show that our proposed method works better than GLRAM. Also, applying this approach to other multilinear dimension reduction methods like MPCA and MLDA is straightforwar